Definitely do NOT eat at the Posejdon restaurant in the old city centre. Awful tourist trap with over-priced sub-standard food.
If you're there for a few days I'd recommend getting the ferry to Brac for the day and/or driving along the coast to Omis for nice beaches. You can also do white water rafting there which is great fun.
Split is a bit if a dump itself but there are plenty of nice places just a short bus ride away.
Travel about half an hour outside of Split by car/taxi/bus to visit the UNESCO world heritage site at Trogir, its a Venetian walled city with excellent shops, bars and restaurants all situated around a lovely marina.